How many ways can one arrange the word EDUCATION such that relative positions of vowels and consonants remains same

The word EDUCATION is a 9 letter word, with none of the letters repeating.

The vowels occupy 3, 5, 7th and 8th position in the word and the remaining 5 positions are occupied by consonants

As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the aforementioned 4 places and the consonants can occupy 1st, 2nd, 4th, 6th and 9th positions.

The 4 vowels can be arranged in the 3rd, 5th, 7th and 8th position in 4! Ways.

Similarly, the 5 consonants can be arranged in 1st, 2nd, 4th, 6th and 9th position in 5! Ways.

Hence, the total number of ways = 4! * 5! = 2880
10 years agoHelpfull: Yes(11) No(7)
here total vowel = 5 so they can arrange in 5! ways
and constant= 4 so they can arrange in 4! ways
so total np of ways= 5! X 4!=2880
10 years agoHelpfull: Yes(9) No(2)
ans:
2*5!*4!
10 years agoHelpfull: Yes(4) No(9)
5P5*4P4
= 5!*4!
=2880
10 years agoHelpfull: Yes(2) No(0)
5! Vowel
4!consonant
Multiply them =2880
10 years agoHelpfull: Yes(1) No(0)
arragement will be 5! ways for vowel
and 4! ways for consonent
so 5!*4!=2880 ways
10 years agoHelpfull: Yes(1) No(0)
total 5!*5!
dctn are consonents * vowels (4+1)!*(5!)
9 years agoHelpfull: Yes(1) No(0)
5P5*4P4
= 5!*4!
=2880
10 years agoHelpfull: Yes(0) No(0)
total number of ways= 5! X 4!=2880
9 years agoHelpfull: Yes(0) No(0)
5!+4!+4!+3!+3!+2!+2!+1!+1!= 186
9 years agoHelpfull: Yes(0) No(2)

How many ways can one arrange the word EDUCATION such that relative positions of vowels and consonants remains same?